US11790261B2 - Tunable coupling between a readout cavity and a parametric amplifier to enhance qubit measurements - Google Patents
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- US11790261B2 US11790261B2 US17/192,479 US202117192479A US11790261B2 US 11790261 B2 US11790261 B2 US 11790261B2 US 202117192479 A US202117192479 A US 202117192479A US 11790261 B2 US11790261 B2 US 11790261B2
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- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
- G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
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- G06—COMPUTING; CALCULATING OR COUNTING
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- G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
- G06N10/70—Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
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- H03F—AMPLIFIERS
- H03F19/00—Amplifiers using superconductivity effects
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- aspects of the disclosure are related to the field of quantum computing devices and in particular, to an amplification device that improves the measurement of qubits.
- Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction.
- One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators—magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Unfortunately, these nonreciprocal elements have limited performance and are not easily integrated on chip.
- a superconducting amplifier device comprises a parametric amplifier and a tunable coupling between the parametric amplifier and a readout cavity external to the superconducting amplifier device.
- the tunable coupling allows an entangled signal, associated with a qubit in the readout cavity, to transfer from the readout cavity to the parametric amplifier.
- the parametric amplifier amplifies the entangled signal to produce an amplified signal (entangled or not) as output to a measurement sub-system.
- FIG. 1 illustrates a quantum computing environment in an implementation.
- FIG. 2 illustrates an operational scenario in an implementation.
- FIGS. 3 - 5 illustrate exemplary characterizations of the operation a superconducting amplifier device in an implementation.
- FIG. 6 illustrates a chip layout in an implementation.
- FIG. 7 illustrates an optical micrograph an implementation.
- FIG. 8 illustrates an experimental schematic in an implementation.
- FIG. 9 illustrates an alternative device design in an implementation.
- tunable coupling between the readout cavity and the amplifier device may be provided by—for example—a superconducting switch, superconducting junction-based couplers, variable microwave-frequency couplers, or any other suitable coupling.
- the tunable coupling allows an entangled signal, associated with a qubit in the readout cavity, to transfer from the readout cavity to a parametric amplifier in the amplifier device.
- the parametric amplifier amplifies the entangled signal to produce an amplified signal which may then be output to a measurement sub-system. Entanglement may be preserved in some scenarios but lost in others during amplification as preserving entanglement is not required for the disclosed readout to succeed.
- a second tunable coupling may be provided between the parametric amplifier and measurement sub-system to allow the amplified signal to reach the measurement sub-system, although such a coupling need not be tunable.
- a superconducting switch or other suitable tunable coupling mechanism provide for control over the coupling between a qubit and amplifier. Doing so allows a transmon qubit to be measured using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and more efficient compared to existing superconducting qubit measurements. As such, these solutions provide a high-quality platform for the scalable measurement of superconducting qubits.
- Qubit-specific projective measurement is a requirement for scalable quantum computation and quantum error correction.
- qubit measurement generally involves scattering a microwave pulse off of a readout cavity dispersively coupled to the qubit. This pulse is routed through ferrite circulators and/or isolators to a Josephson-junction-based parametric amplifier, sent to room temperature, and digitized.
- This readout scheme can work well: it is low backaction, quantum nondemolition, and can have infidelity of 10 ⁇ circumflex over ( ) ⁇ ( ⁇ 2) in less than 100 ns, with the best reported infidelity of less than 10 ⁇ circumflex over ( ) ⁇ ( ⁇ 4). Challenges arise, however, as the scale and requirements of superconducting quantum systems increase.
- ferrite circulators are bulky and their requisite number scales linearly with the number of measurement channels. Fitting enough circulators at the base temperature stage of a cryostat is one eventual bottleneck associated with building a scalable quantum computer.
- circulators are both lossy and provide finite isolation from amplifier noise. Isolation can be improved using multiple isolators in series, but at the cost of increased resistive loss and impedance mismatches, which necessitate a stronger readout pulse in order to make a projective qubit measurement. This can be just as detrimental as amplifier backaction; both have the potential to drive higher-level state transitions which can cause readout errors and reduce the extent to which a measurement is quantum nondemolition.
- a replacement for ferrites is proposed herein that is based on the coordinated operation of superconducting switches.
- These switches are integrated into a single, chip-scale device referred to herein as a ‘superconducting isolating modular bifurcation amplifier’ (SIMBA), illustrated in FIG. 1 .
- SIMBA superconducting isolating modular bifurcation amplifier
- FIG. 1 a quantum computing environment 100 includes a SIMBA, represented by amplifier device 101 , which itself includes a two-port parametric cavity (a Josephson parametric amplifier), represented by parametric cavity 107 .
- Amplifier device 101 also includes two fast, low-loss and high on-off ratio superconducting switches placed on both ports of amplifier device 101 , represented by switch 103 and switch 105 respectively.
- parametric cavity 107 Central to amplifier device 101 is parametric cavity 107 , which is a flux-pumped parametric cavity comprising a lumped-element inductor-capacitor circuit where approximately half the inductance comes from an array of superconducting quantum interference devices (SQUIDs).
- the parametric cavity resonant frequency can be tuned between 4 and 7.1 GHz by applying an external magnetic flux. When flux through these SQUIDs is modulated at twice the cavity resonance frequency, the cavity state undergoes phase-sensitive parametric amplification via three-wave mixing.
- the external coupling of parametric cavity 107 is controlled by superconducting switches (switch 103 and switch 105 ) constructed using a ‘tunable inductor bridge’ (TIB). TIB transmission is tuned by a dc signal which changes the balance of a Wheatstone bridge of SQUID arrays.
- the speed at which transmission can be tuned is limited by off-chip, low-pass filters with a 350-MHz cutoff frequency placed on the TIB bias lines.
- the TIB has an on/off ratio greater than 50 dB tunable between 4 and 7.3 GHz. This overlaps with the range over which parametric cavity 107 can be tuned, allowing the amplifier device 101 itself to be tuned to operate over several GHz.
- the TIB 1-dB compression point is approximately ⁇ 98 dBm, which crucially allows the TIB to function effectively while the state in the parametric cavity is amplified.
- FIG. 2 illustrates the operations 200 of a superconducting amplifier device as contemplated herein (e.g., amplifier device 101 ).
- a superconducting amplifier device as contemplated herein (e.g., amplifier device 101 ).
- Such a device may be used to measure a transmon qubit dispersively coupled to a readout cavity.
- a pulse is first sent into the weakly coupled port 112 of a two-port readout cavity, where it acquires a qubit-state-dependent phase shift.
- Switch 103 (TIB 1 ) is then set to transmit mode for a duration (20 ns), chosen to fully swap this pulse into the parametric cavity 107 , which has previously been tuned near resonance.
- the parametric cavity 107 is then strongly flux pumped into the bistable regime: a nonunitary process in which the cavity latches into one of two bistable states with opposite phase but large, equal amplitudes.
- Readout is achieved by seeding the parametric cavity state with the probe tone, such that the postmeasurement qubit state is correlated with the latched state of the parametric cavity 107 .
- This design discretizes and stores the measurement result within the cryostat as a step toward implementing rapid and hardware efficient feed-forward protocols.
- switch 105 TIB 2
- switch 105 is set to transmit mode, coupling this state to a standard cryogenic microwave measurement chain or other such measurement sub-system.
- Three figures of merit describe the success of this readout: excess backaction nb, measurement efficiency ⁇ , and maximum readout fidelity F 0 .
- a framework of measurement-induced dephasing characterizes these quantities.
- measurement-induced dephasing of the qubit comes only from a readout pulse.
- ⁇ 1 > are coherent states both of amplitude
- , separated in phase space by the angle 2 ⁇ 2 arctan (2 ⁇ / ⁇ r ), where the readout cavity frequency shifts by ⁇ /2 ⁇ dependent on the qubit state, and ⁇ r /2 ⁇ is the loss rate of the readout cavity.
- n r (
- n r is nearly equal to the readout pulse photon number
- measurement may include “excess backaction” or additional dephasing. This is modeled as an additional pulse with an effective photon number,
- n b - 1 2 ⁇ log ⁇ ( 2 ⁇ ⁇ b ) ( 1 )
- measurement efficiency ⁇ is determined by the readout fidelity of a weak measurement (quantified by v), compared to its backaction (quantified by a).
- nb, ⁇ , and F 0 readout fidelity and postmeasurement coherence were measured, both as functions of the experimental readout amplitude.
- FIGS. 3 - 5 illustrate various characterizations of the experimental operations.
- characterization 300 illustrates one or more operations whereby post-measurement qubit coherence
- characterization 400 illustrates one or more operations whereby excess backaction is determined by inserting a “measurement” with zero readout amplitude. Post-measurement coherence after excess backaction with the parametric cavity pump on and off, are compared to a case with no backaction (no readout pulse, pump, or TIB switching inserted in the Ramsey sequence, violet).
- no backaction no readout pulse, pump, or TIB switching inserted in the Ramsey sequence, violet.
- characterization 500 illustrates one or more operations whereby post-measurement coherence
- is measured both with the parametric pump turned on or off during the variable measurement sequence.
- and determines the excess backaction n b ⁇ log(2 ⁇ b )/2.
- Measurement efficiency ⁇ is determined by a comparison between measurement-induced dephasing and readout fidelity while sweeping readout amplitude.
- readout fidelity F r is computed by measuring P(e
- the qubit is prepared in a superposition state, exposed to backaction from a variable strength measurement with readout pulse amplitude ⁇ square root over (n r ) ⁇ , and then projectively measured after a variable Ramsey delay and a second ⁇ /2 pulse.
- the sweep repeats over the variable amplitude, both with the parametric pump turned off and on during the variable measurement.
- qubit coherence is also measured without exposure to any backaction, meaning no variable measurement inserted into the Ramsey delay (e.g., FIG. 4 ).
- the ratio of the Ramsey fringe amplitudes with or without exposure to backaction gives 2
- This transmission is higher than the ⁇ 50 dB of transmission measured in a single TIB in isolation, a discrepancy which may result from the solvable problems of a spurious transmission path within the chip or sample box, or the pumped parametric cavity state approaching the power handling capability of the TIB.
- Maximum readout fidelity is limited by qubit decay and state preparation error including a ⁇ 2% thermal population, errors which do not represent limitations of the SIMBA itself.
- efficiency is limited primarily by the 4.0 MHz ⁇ 0.2 MHz loss rate of the parametric cavity. The dominant contributions to this loss are the nonzero transmission through TIB 2 when in reflect mode, on-chip dissipation, and coupling to cable modes: effects which may all be mitigated.
- the transmon qubit is measured using a chip-scale, pulsed directional amplifier as disclosed herein.
- the qubit is isolated from amplifier backaction using a superconducting switch to control the coupling between a readout and parametric cavity. Simultaneously demonstrated metrics for this readout are given in Table I.
- n b ⁇ 0.02 With reasonable changes to the SIMBA and experimental setup, it is possible to achieve ⁇ >90% with F 0 >99%, n b ⁇ 0.02 and a measurement time of less than 100 ns.
- This demonstration combines state-of-the-art measurement efficiency and considerable isolation from amplifier backaction such that n b ⁇ n r proj /4.
- the SIMBA is chip scale, compatible with scalable fabrication procedures including the use of through-silicon vias and requires only one microwave control tone to operate. The SIMBA is therefore a favorable choice for high-quality and scalable superconducting qubit measurement.
- FIG. 6 A layout 600 of a SIMBA chip 601 is shown in FIG. 6 , and an optical micrograph 700 of the device is shown in FIG. 7 .
- the SIMBA chip 601 includes two TIBs ( 603 , 605 ) and a JPA 607 .
- a micrograph of the region within the smaller dashed line is shown in FIG. 7 .
- the SIMBA chip extends 2.5 mm to the right of the region illustrated here, such that the wire bonding pads for the ‘JPA uniform bias’ and ‘JPA pump’ lines are not shown.
- the internal design of the TIB allows it to function as a simple microwave switch.
- the TIBs disclosed herein are significantly improved.
- past TIBs had a chipmode around 5 GHz (near to the qubit frequency in the SIMBA experiment discussed herein) and had greater loss out of their bias lines due to a lack of any on-chip, low-pass filters on these lines.
- the TIB can be thought of as a superconducting analog to a microwave mixer, with diodes replaced by SQUID arrays.
- the TIB functions as a microwave switching/modulation element where symmetry of a Wheatstone bridge allows for high performance, broadband operation.
- the process of preserving vs. breaking the symmetry of the bridge allows for transmission through the TIB to be tuned by a far greater ratio than its constituent inductors can be tuned.
- a lumped-element schematic 710 of a TIB is shown in FIG. 7 .
- a balun couples the left port of the TIB to the differential voltage across the top and bottom nodes of the bridge (nodes a and c). No signal can couple between the two ports when the bridge is balanced, meaning that all four bridge inductors have equal value. To see this, consider an oscillating signal of amplitude v applied at the left port of the lumped element circuit in FIG. 7 .
- the Wheatstone bridge 711 is twisted into a figure-eight geometry in order to tune the bridge imbalance with a single bias line while preserving as much symmetry in the circuit as possible.
- This bias line runs through the center of the figure-eight and puts a gradiometric flux g into the SQUID arrays on opposite sides of the bridge. At the same time, all the arrays see an identical uniform background flux u.
- Gradiometric bias lines in FIG. 7 contain a low-pass filter (LPF 714 ), realized with a 20 nH spiral inductor. This filter limits microwave power coupling out of the bias line.
- LPF 714 low-pass filter
- This filter limits microwave power coupling out of the bias line.
- a numerical finite-element simulation indicates that this inductor has a self-resonance frequency of 7.9 GHz (note that in this style of inductive filter, a higher inductance will generally lead to a lower self-resonance frequency). Further simulations indicate that bias port is generally smaller than ⁇ 40 dB between 4 and 8 GHz with inclusion of this LPF, but as high as ⁇ 20 dB without it.
- transmission from a microwave port of a TIB out of its gradiometric bias port is simulated to be between ⁇ 39 dB and ⁇ 47 dB (the exact value changes slightly depending on which of the two microwave ports is used, and whether the TIB is in transmit or reflect mode).
- the TIBs used in this work contain a second on-chip bias line for applying a dc uniform flux u. This bias line also contains two LPFs.
- FIG. 7 also includes a lumped element schematic 720 of the JPA is shown in FIG. 7 .
- a resonator is formed by an inductor (realized with a SQUID array similar to that in the TIBs), with 430 fF capacitors to ground on either side.
- the SQUID array inductance is biased to be minimum, the array has an inductance of 0.66 nH.
- the geometric inductance of the resonator is 0.52 nH.
- flux through these SQUIDs is modulated at twice the JPA resonance frequency using a microwave bias line, which contains an on-chip capacitor to block dc-current.
- a fingered capacitor 80 fF is placed between the JPA and each TIB, which may limit the coupling rate.
- the JPA is configured and/or characterized by setting TIB 2 to transmit mode and measuring in reflection off of TIB 2 . Doing so, the JPA frequency is tunable between approximately 4 and 7 GHz, a similar range over which the TIB is designed to operate.
- the SIMBA may therefore be tuned to operate over a several GHz frequency range.
- the following describes a process employing a SIMBA to measure a superconducting qubit, beginning with calibration.
- the calibration procedure for superconducting qubit readout using a SIMBA is summarized below.
- the first three steps are generally true of any readout scheme which uses a tunable, narrow band and phase sensitive parametric amplifier.
- the final two steps are SIMBA-specific.
- the reflect modes of both TIBs occur when current in their gradiometric bias lines is set near zero. This can be quickly checked by measuring transmission through the readout cavity while sweeping the gradiometric flux bias on either TIB 1 or TIB 2 with the other fixed. In practice, the optimal reflect mode may occur when this current is slightly offset from zero.
- Measurement of excess backaction at this operating point is a measure of the isolation provided by TIB 1 .
- This isolation can alternatively be measured by the following procedure: the qubit is prepared in the excited state, and then projectively measured after a delay placed between the readout pulse and the rest of the measurement procedure. The resulting oscillations correspond to the readout pulse swapping back and forth between the readout and parametric cavities when TIB 1 is in reflect mode. The average measured swap time is 380 ns.
- one commercial cryogenic ferrite circulator provides ⁇ 18 dB of isolation.
- QND-ness is defined as the likelihood for a measured qubit to remain in its measured eigenstate. It is important that a measurement is QND when a qubit must be repeatedly measured, for instance in measurement-based quantum error correction schemes. In practice, a measurement can be non-QND by kicking the qubit out of its two-level subspace. In general, these effects can become pronounced in readout schemes which require high amplitude readout pulses or have too much backaction.
- the qubit, readout cavity and SIMBA are placed inside of a cryoperm can at the base temperature stage of a dilution refrigerator.
- a complete experimental schematic 800 for qubit readout using a SIMBA is shown in FIG. 8 .
- Eccosorb filters are placed on the lines running in and out of the qubit+readout cavity+SIMBA system, in order to shield the qubit from high-frequency radiation.
- the SIMBA may be placed as close as possible to the readout cavity in order to minimize the electrical length between them. If any mode formed by this electrical length falls close in frequency to the readout/parametric cavity frequency, a significant fraction of the readout pulse can also couple into it. This lowers the measurement efficiency and can complicate the calibration procedure.
- the strongly coupled port of the readout cavity is constructed using an SMA connector, which is then screwed directly into another SMA connector on the SIMBA sample box. This results in approximately 3 cm of waveguide between the readout cavity and SIMBA chip. This length may be significantly shortened in future designs by engineering a more compact connection mechanism.
- a SIMBA demonstrates superconducting qubit readout with state-of-the-art measurement efficiency and low excess backaction.
- the combination of these features is achieved without any ferrite circulator or isolator placed between the qubit and parametric amplifier. Readout is also fast, high fidelity and largely quantum non-demolition.
- the SIMBA is a promising platform for scalable superconducting qubit measurement.
- FIG. 9 An alternative design different than discussed elsewhere in this work is discussed and illustrated in FIG. 9 .
- This arrangement 900 is the same as in FIG. 1 , except that it uses a SIMBA 901 constructed from a one-port JPA 902 connected to two TIBs ( 903 , 904 ) via a microwave T-junction.
- the JPA and TIBs are on separate chips, connected together on the same printed circuit board.
- the measurement efficiency and readout fidelity of qubit readout demonstrated in this setup compare unfavorably to the readout demonstrated in the main text. Additionally, the calibration of this device was complicated both by the significant presence of trapped flux vorticies near the Josephson parametric amplifier, and by the microwave T-junction between the TIBs and JPA.
- Readout using a SIMBA can be improved to be significantly faster than the 265 ns measurement time reported in this work without detriment to the readout performance.
- Dispersive readout using a SIMBA is different from standard dispersive readout schemes because the external coupling rate is now tunable.
- the readout cavity external coupling can be made large during the measurement allowing for a fast readout but is otherwise tuned close to zero so that the qubit T 1 time is not limited, obviating the need for a Purcell filter.
- aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.
- the tunable coupling(s) disclosed herein comprise(s) a first superconducting switch and/or a second superconducting switch and the parametric amplifier comprises a parametric cavity having one or more ports.
- the first superconducting switch may be coupled to the parametric cavity via a first port and the second superconducting switch is coupled to the parametric cavity via a second port.
- both the first superconducting switch and the second superconducting switch may be coupled to the parametric cavity via the same port.
- an exemplary superconducting amplifier device may be integrated onto one or more chips or integrated circuits.
- a single integrated circuit could include the parametric cavity, the first superconducting switch, and the second superconducting switch.
- the parametric cavity may be integrated on one chip, while the switches may be integrated on one or more other chips.
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Abstract
Description
where nr=(|α| sin θ)2 is the effective photon number of the readout pulse, corresponding to the square of half the separation in phase space between |α0> and |α1>. Here, nr is nearly equal to the readout pulse photon number |α|2 Because 2χ/2π=1.93 MHz and κr/2π=440 kHz, so that nr=0.95|α|2. In practice, measurement may include “excess backaction” or additional dephasing. This is modeled as an additional pulse with an effective photon number,
A dephased qubit indicates that information about its energy eigenstate may be learned by a detector. This information may be quantified by a readout fidelity,
F r=1−P(e|π)−P(g|π) (3)
F r =F 0 erf[√{square root over (2ηn r)}]=F 0 erf[vϵ] (4)
η=2σ2 v 2 (5)
TABLE 1 |
Readout performance summary. |
Parameter | Value | ||
Measurement efficiency | η = 70.4% ± 0.9% | ||
Excess backaction | nb = 0.66 ± 0.01 photons | ||
Maximum readout fidelity | F0 = 95.5% ± 0.3% | ||
Measurement time | 265 ns | ||
-
- 1. Tune the JPA frequency to the readout cavity frequency.
- 2. Sweep the JPA pump amplitude such that the JPA gives desired gain/bifurcation.
- 3. Choose the readout pulse amplitude and frequency, and the qubit pulse amplitude and frequency. Because the SIMBA is a phase-sensitive amplifier, the phase difference between the readout tone and the pump tone may be calibrated.
- 4. To optimize readout fidelity, sweep the duration for which TIB1 is set to transmit mode.
- 5. Fine-tune TIB reflect modes to minimize backaction, and to maximize the measurement efficiency.
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